Astronomy & Celestial Mechanics
the sky, computed
Concept

Self-calibration — where it appears

Determining an instrument's response from the observations themselves, by requiring that repeated measurements of the same objects agree. It removes the need for an external standard and leaves undetermined whatever pattern the observing strategy cannot distinguish from the sky.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

20 closure phases, unmoved by an atmosphere that ruins every baseline. Closure phase measured against closure phase true, for all 20 triangles of a 6-antenna array observing a binary 3.2 mas apart with a flux ratio of 0.35. Each antenna has been given an independent atmospheric phase of 65° rms, which corrupts the individual baseline phases by 102° rms — several times the 31.2° the source itself produces, so no single visibility phase in this simulation carries usable information. Every point here nonetheless sits exactly on the diagonal: the per-antenna terms cancel identically round any triangle, and the largest departure over all 20 is 2.5e-14 degrees, which is round-off. The price is in the counting. 6 antennas give 15 baseline phases of which 5 are consumed by the unknowns, so of the 20 triangles only 10 closures are independent — a fraction (N−2)/N = 0.667 of the phase information. For two antennas that fraction is zero and there is no closure at all; the Event Horizon Telescope's image rests on quantities of this kind and on no absolute phase whatever.

A phase that survives what corrupts it

An atmosphere over each antenna adds an unknown to the phase of every baseline that antenna takes part in. Sum the phases round a triangle and every one of those unknowns cancels identically — which is the reason an image can be made across ten thousand kilometres, and the reason it has no position on the sky.

starlight · Interferometry A dome flat that is 3.5 per cent wrong leaves 0.042 magnitudes across the field. Two things called the flat field. The left panel is the true illumination of the focal plane, falling by 12 per cent from centre to corner because of vignetting and the filter's own radial transmission. The middle panel is what a dome flat measures, which is the illumination produced by a screen at a finite distance lit by lamps — a different angular distribution, and therefore a different fall-off by a few per cent. The right-hand plot is what survives dividing one by the other: a smooth radial gradient of 0.042 magnitudes from centre to edge. Pixel-to-pixel response scatter, which is what most people mean by a flat field, is 1.8 per cent per pixel and averages down to 0.255 per cent inside a photometric aperture. The term everybody removes is the one that does not matter, and the term that matters is smooth, is different for every flat-fielding method, and looks exactly like a real gradient in the sky.

A response measured pixel by pixel

Two completely different quantities are called the flat field. One is the detector's pixel-to-pixel response, which everybody removes and which averages away anyway. The other is the illumination pattern of the optics, which is smooth, is different for every method of measuring it, and survives into every magnitude the instrument produces.

starlight · Photometric systems A flat sky, and stars that are wrong. The residual brightness after flat-fielding, in per cent, against distance from the field centre, for the sky (flat line) and for a star (curve), with 3 per cent scattered light at the centre of both the flat and the science exposure. The sky, which fills the field as the flat's illumination did, carries the same scattered component and divides out exactly: the corrected image looks perfectly flat, which is the test an observer applies. The star, a point that scatters a negligible fraction of its light into its own aperture, is divided by the scattered component it never had and comes out 2.9 per cent too faint at the centre. The visible check passes and the measurement fails.

Light that adds, corrected as if it multiplied

A flat field is an exposure of something uniform, and some of the light in it did not come through the optics the way starlight does — it scattered off a baffle, a filter face or a dusty window and landed where the geometry never sent it. Dividing by that flat makes the sky in every science image look perfect and makes every star in it wrong, by an amount the image itself cannot show.

starlight · Photometric systems

Named alongside it

The objects these essays reach for when they reach for this one.

Flat fieldIllumination correctionScattered lightSystematic errorAntenna gainAperture synthesisAstrometric referenceAtmospheric coherence timeClosure amplitudeClosure phaseColour termDegrees of freedom

All concepts